Angular rate of rotation about a given coordinate axis may be measured by moving (e.g., vibrating) an accelerometer along an axis normal to the accelerometer's sensitive axis and normal to the rate axis about which rotation is to be measured. For example, consider a set of X, Y, Z coordinate axes fixed in a body whose rotation rate is to be measured, and an accelerometer also fixed in the body with its sensitive axis aligned along the Z axis. If the angular rotation vector of the body includes a component along the X axis, then periodic motion of the accelerometer along the Y axis will result in a periodic Coriolis acceleration acting in the Z direction that will be sensed by the accelerometer. The magnitude of the Coriolis acceleration is proportional to the velocity along the Y axis and the rotation rate about the X axis. As a result, the output of the accelerometer includes a DC or slowly changing component that represents the linear acceleration of the body along the Z axis, and a periodic component that represents the rotation of the body about the X axis. The accelerometer output can be processed, along with the outputs of accelerometers that have their sensitive axes in the X and Y directions and that are moved along the Z and X axes, respectively, to yield linear acceleration and angular rate about the X, Y and Z axes. Such signal processing is described in U.S. Pat. Nos. 4,445,375 and 4,590,801.
As described in U.S. Pat. No. 4,590,801, one preferred embodiment of a rotation rate sensor comprises, for each axis, two accelerometers oriented with their sensitive axes parallel or antiparallel to one another, and means for vibrating the accelerometers along an axis normal to their sensitive axes. A suitable method for vibrating such accelerometer pairs is described in U.S. Pat. No. 4,510,802. In the system described in that patent, a parallelogram structure is used to vibrate the accelerometers along a common vibration axis. In such an arrangement, it may be demonstrated that a bias error is produced by interaction between misalignment of the accelerometers with respect to the desired sensitive axis, and the phase shift between the motion of the accelerometers and their resulting output signals. This bias error results from the fact that the misalignment causes the accelerometer to sense a component of the acceleration used to vibrate the accelerometers. In the absence of any phase shift, this component is synchronous with the acceleration caused by the vibration, and therefore 90.degree. out of phase with the vibration velocity and therefore with the Coriolis acceleration. The vibration acceleration therefore would be cancelled in the rate channel. However because of the phase shift introduced by the accelerometer between its vibration velocity and the Coriolis component of its output signal, the vibration acceleration component is phase shifted so that it includes a subcomponent that is in phase with the vibration velocity, and that therefore shows up in the rate channel. This interaction between misalignment and phase shift is the largest source of bias error in an angular rate sensor of this type.
An approach to eliminating the above-described rate bias is set forth in U.S. Pat. No. 4,665,748. In the system described in that patent, the angular rate output of the accelerometers is demodulated by a signal in phase with the accelerometer motion, to produce a feedback signal that is used to drive the components of the accelerometer output signal that are synchronous with the accelerometer motion toward a null value. The present invention relates to an improved technique for reducing the bias error caused by interaction between misalignment and phase shift of the accelerometers.